Cryptology ePrint Archive: Report 2008/108

Abstract: A recently proposed class of multivariate quadratic schemes, the
Rainbow-Like signature Schemes, in which successive sets of central
variables are obtained from previous ones by solving linear
equations, seem to lead to efficient schemes (TTS, TRMS, and
Rainbow) that perform well on systems of low computational
resources. Recently SFLASH ($C^{\ast-}$) was broken by Dubois,
Fouque, Shamir, and Stern via a differential attack. In this paper,
we exhibit similar attacks based on differentials, that will reduce
published Rainbow-like schemes below their security levels. We will
present a new type of construction of Rainbow-Like schemes and
design signature schemes with new parameters for practical
applications.